Spartan (chemistry software)

Spartan

Spartan graphical user interface

Developer(s)| Wavefunction, Inc.[1] & Q-Chem
Initial release| 1991; 35 years ago (1991)
Stable release|

Spartan'20 v.1.1 / 2021; 5 years ago (2021)

Written in| C, C++, Fortran, Qt
Operating system| Windows, Mac OS X, Linux
Platform| x86-64
Available in| English
Type| Molecular modelling, computational chemistry
License| Proprietary commercial software
Website| www.wavefun.com

Spartan is a molecular modelling and computational chemistry application from Wavefunction.[2] It contains code for molecular mechanics, semi-empirical methods, ab initio models,[3] density functional models,[4] post-Hartree–Fock models,[5] and thermochemical recipes including G3(MP2)[6] and T1.[7] Quantum chemistry calculations in Spartan are powered by Q-Chem.[8]

Primary functions are to supply information about structures, relative stabilities and other properties of isolated molecules. Molecular mechanics calculations on complex molecules are common in the chemical community. Quantum chemical calculations, including Hartree–Fock method molecular orbital calculations, but especially calculations that include electronic correlation, are more time-consuming in comparison.

Quantum chemical calculations are also called upon to furnish information about mechanisms and product distributions of chemical reactions, either directly by calculations on transition states, or based on Hammond's postulate,[9] by modeling the steric and electronic demands of the reactants. Quantitative calculations, leading directly to information about the geometries of transition states, and about reaction mechanisms in general, are increasingly common, while qualitative models are still needed for systems that are too large to be subjected to more rigorous treatments. Quantum chemical calculations can supply information to complement existing experimental data or replace it altogether, for example, atomic charges for quantitative structure-activity relationship (QSAR)[10] analyses, and intermolecular potentials for molecular mechanics and molecular dynamics calculations.

Spartan applies computational chemistry methods (theoretical models) to many standard tasks that provide calculated data applicable to the determination of molecular shape conformation, structure (equilibrium and transition state geometry), NMR, IR, Raman, and UV-visible spectra, molecular (and atomic) properties, reactivity, and selectivity.

## Contents

* 1 Computational abilities
* 2 Tasks performed
* 3 Graphical user interface
* 4 Graphical models
* 5 Spectral calculations
* 6 Databases
* 7 Major release history
* 7.1 Windows, Macintosh, Linux versions
* 8 See also
* 9 References
* 10 External links

## Computational abilities

This software provides the molecular mechanics, Merck Molecular Force Field (MMFF),[11] (for validation test suite), MMFF with extensions, and SYBYL,[12] force fields calculation, Semi-empirical calculations, MNDO/MNDO(D),[13] Austin Model 1 (AM1),[14] PM3,[15][16][17][18] Recife Model 1 (RM1)[19] PM6.[20]

* Hartree–Fock, self-consistent field (SCF) methods, available with implicit solvent (SM8).[21]
* Restricted, unrestricted, and restricted open-shell Hartree–Fock
* Density functional theory (DFT) methods, available with implicit solvent (SM8).[21]
* Standard functionals: BP,[22][23] BLYP,[22][24] B3LYP,[22][24][25] EDF1,[26] EDF2,[27] M06,[28] ωB97X-D[29]

The calculated T1[7] heat of formation (y axis) relative to the experimental heat of formation (x axis) for a set of >1800 diverse organic molecules from the NIST thermochemical database[30] with mean absolute and RMS errors of 8.5 and 11.5 kJ/mol, respectively.

*     * Exchange functionals: HF, Slater-Dirac,[31] Becke88,[22] Gill96,[32] GG99,[33] B(EDF1), PW91[34]
* Correlation functionals: VWN,[35] LYP,[24] PW91,[36] P86,[37] PZ81,[38] PBE.[39]
* Combination or hybrid functionals: B3PW91,[40] B3LYP,[25] B3LYP5, EDF1,[26] EDF2,[27] BMK[41]
* Truhlar group[42] functionals: M05,[43] M05-2X,[43] M06,[28] M06-L [44] M06-2X,[28] M06-HF[45]
* Head-Gordon group functionals:[46] ωB97,[47] ωB97X,[47] ωB97X-D[29]
* Coupled cluster methods.
* CCSD,[48] CCSD(T),[49] CCSD(2),[50] OD,[51] OD(T), OD(2),[52] QCCD,[53] VOD,[54] VOD(2),[54] VQCCD[54]
* Møller–Plesset methods.
* MP2,[55][56] MP3,[57][58] MP4,[59] RI-MP2[60][61][62]
* Excited state methods.
* Time-dependent density functional theory (TDDFT)[63][64]
* Configuration interaction: CIS,[65] CIS(D),[66] QCIS(D),[67] quadratic configuration interaction (QCISD(T)),[67] RI-CIS(D)[68]
* Quantum chemistry composite methods, thermochemical recipes.
* T1,[7] G2,[69] G3,[70] G3(MP2)[6]

## Tasks performed

Available computational models provide molecular, thermodynamic, QSAR, atomic, graphical, and spectral properties. A calculation dialogue provides access to the following computational tasks:

* Energy[71] – For a given geometry, provides energy and associated properties of a molecule or system. If quantum chemical models are employed, the wave function is calculated.
* Equilibrium molecular geometry[72] \- Locates the nearest local minimum and provides energy and associated properties.
* Transition state geometry[72] \- Locates the nearest first-order saddle point (a maximum in a single dimension and minima in all others) and provides energy and associated properties.
* Equilibrium conformer[72] – Locates lowest-energy conformation. Often performed before calculating structure using a quantum chemical model.
* Conformer distribution[71] – Obtains a selection of low-energy conformers. Commonly used to identify the shapes a specific molecule is likely to adopt and to determine a Boltzmann distribution for calculating average molecular properties.
* Conformer library[71] – Locates lowest-energy conformer and associates this with a set of conformers spanning all shapes accessible to the molecule without regard to energy. Used to build libraries for similarity analysis.
* Energy profile[71] – Steps a molecule or system through a user defined coordinate set, providing equilibrium geometries for each step (subject to user-specified constraints).
* Similarity analysis[71] – quantifies the likeness of molecules (and optionally their conformers) based on either structure or chemical function (Hydrogen bond acceptors–donors, positive–negative ionizables, hydrophobes, aromatics). Quantifies likeness of a molecule (and optionally its conformers) to a pharmacophore.

## Graphical user interface

The software contains an integrated graphical user interface. Touch screen operations are supported for Windows 7 and 8 devices. Construction of molecules in 3D is facilitated with molecule builders (included are organic, inorganic, peptide, nucleotide, and substituent builders). 2D construction is supported for organic molecules with a 2D sketch palette. The Windows version interface can access ChemDraw; which versions 9.0 or later may also be used for molecule building in 2D. A calculations dialogue is used for specification of task and computational method. Data from calculations are displayed in dialogues, or as text output. Additional data analysis, including linear regression, is possible from an internal spreadsheet.[71]

## Graphical models

A cut-away view of the electrostatic potential map of fullerene (C60), the blue area inside the molecule is an area of positive charge (relative to the superstructure, providing a pictorial explanation for fullerene's ability to encapsulate negatively charged species).

Graphical models, especially molecular orbitals, electron density, and electrostatic potential maps, are a routine means of molecular visualization in chemistry education.[73][74][75][76][77]

* Surfaces:
* Molecular orbitals (highest occupied, lowest unoccupied, and others)
* Electron density – The density, ρ(r), is a function of the coordinates r, defined such that ρ(r)dr is the number of electrons inside a small volume dr. This is what is measured in an X-ray diffraction experiment. The density may be portrayed in terms of an isosurface (isodensity surface) with the size and shape of the surface being given by the value (or percentage of enclosure) of the electron density.
* Spin density – The density, ρspin(r), is defined as the difference in electron density formed by electrons of α spin, ρα(r), and the electron density formed by electrons of β spin, ρβ(r). For closed-shell molecules (in which all electrons are paired), the spin density is zero everywhere. For open-shell molecules (in which one or more electrons are unpaired), the spin density indicates the distribution of unpaired electrons. Spin density is an indicator of reactivity of radicals.[72]
* Van der Waals radius (surface)
* Solvent accessible surface area
* Electrostatic potential – The potential, εp, is defined as the energy of interaction of a positive point charge located at p with the nuclei and electrons of a molecule. A surface for which the electrostatic potential is negative (a negative potential surface) delineates regions in a molecule which are subject to electrophilic attack.
* Composite surfaces (maps):
* Electrostatic potential map (electrophilic indicator) – The most commonly employed property map is the electrostatic potential map. This gives the potential at locations on a particular surface, most commonly a surface of electron density corresponding to overall molecular size.[71]
* Local ionization potential map – Is defined as the sum over orbital electron densities, ρi(r) times absolute orbital energies, ∈i, and divided by the total electron density, ρ(r). The local ionization potential reflects the relative ease of electron removal ("ionization") at any location around a molecule. For example, a surface of "low" local ionization potential for sulfur tetrafluoride demarks the areas which are most easily ionized.
* LUMO map (nucleophilic indicator) – Maps of molecular orbitals may also lead to graphical indicators. For example, the LUMO map, wherein the (absolute value) of the lowest-unoccupied molecular orbital (the LUMO) is mapped onto a size surface (again, most commonly the electron density), providing an indication of nucleophilic reactivity.

## Spectral calculations

The calculated (DFT/EDF2/6-31G*) IR spectra (red), scaled and optimized to the experimental FT-IR spectra (blue) of phenyl 9-acridinecarboxylate (below).

2D rendering

3D rendering

The molecule phenyl 9-acridinecarboxylate.

Available spectra data and plots for:

* Infrared spectroscopy (IR) spectra
* Fourier transform spectroscopy (FT-IR)[78]
* Raman spectroscopy (IR)[79]
* Nuclear magnetic resonance (NMR) spectra
* 1H chemical shifts[80][81] and coupling constants (empirical)
* 13C chemical shifts,[80][81] Boltzmann averaged shifts, and 13C DEPT spectra
* 2D H vs H Spectra
* COSY[82] plots
* 2D C vs H Spectra
* Heteronuclear single-quantum correlation spectroscopy (HSQC) spectra[83]
* HMBC spectra[84]
* UV/vis Spectra[63][64][65][66][68][85]

Experimental spectra may be imported for comparison with calculated spectra: IR and UV/vis spectra in Joint Committee on Atomic and Molecular Physical Data (JCAMP)[86] (.dx) format and NMR spectra in Chemical Markup Language (.cml) format. Access to public domain spectral databases is available for IR, NMR, and UV/vis spectra.

## Databases

Spartan accesses several external databases.

* Quantum chemical calculations databases:
* Spartan Spectra & Properties Database (SSPD) – a set of about 252,000 molecules, with structures, energies, NMR and IR spectra, and wave functions calculated using the EDF2[27] density functional theory with the 6-31G* basis set.[87]
* Spartan Molecular Database (SMD) – a set of about 100,000 molecules calculated from following models:
* Hartree–Fock with 3-21G, 6-31G*, and 6-311+G** basis sets[87]
* B3LYP[25] density functional with 6-31G* and 6-311+G** basis sets
* EDF1[26] density functional with 6-31G* basis set
* MP2[55] with 6-31G* and 6-311+G** basis sets
* G3(MP2)[6]
* T1[7]
* Experimental databases:
* NMRShiftDB[88] – an open-source database of experimental 1H and 13C chemical shifts.
* Cambridge Structural Database (CSD)[89] \- a large repository of small molecule organic and inorganic experimental crystal structures of about 600,000 entries.
* NIST database[30] of experimental IR and UV/vis spectra.

## Major release history

* 1991 Spartan version 1 Unix
* 1993 Spartan version 2 Unix
* 1994 Mac Spartan Macintosh
* 1995 Spartan version 3 Unix
* 1995 PC Spartan Windows
* 1996 Mac Spartan Plus Macintosh
* 1997 Spartan version 4 Unix
* 1997 PC Spartan Plus Windows
* 1999 Spartan version 5 Unix
* 1999 PC Spartan Pro Windows
* 2000 Mac Spartan Pro Macintosh
* 2002 Spartan'02 Unix, Linux, Windows, Mac

### Windows, Macintosh, Linux versions

* 2004 Spartan'04
* 2006 Spartan'06
* 2008 Spartan'08
* 2010 Spartan'10
* 2013 Spartan'14
* 2016 Spartan'16
* 2018 Spartan'18
* 2021 Spartan'20

## See also

* Q-Chem quantum chemistry software
* Molecular design software
* Molecule editor
* Comparison of software for molecular mechanics modeling
* List of software for Monte Carlo molecular modeling
* Quantum chemistry composite methods
* List of quantum chemistry and solid state physics software

## References

1. ↑ Wavefunction, Inc.
2. ↑ Computational Chemistry, David Young, Wiley-Interscience, 2001. Appendix A. A.1.6 pg 330, Spartan
3. ↑ Hehre, Warren J.; Leo Radom; Paul v.R. Schleyer; John A. Pople (1986). Ab initio molecular orbital theory. John Wiley & Sons. ISBN 0-471-81241-2.
4. ↑ Hohenberg, Pierre; Walter Kohn (1964). "Inhomogeneous electron gas". Physical Review 136 (3B): B864–B871. doi:10.1103/PhysRev.136.B864. Bibcode: 1964PhRv..136..864H.
5. ↑ Cramer, Christopher J. (2002). Essentials of Computational Chemistry. John Wiley & Sons. ISBN 978-0-470-09182-1.
6. ↑ 6.0 6.1 6.2 Larry A. Curtiss; Paul C. Redfern; Krishnan Raghavachari; Vitaly Rassolov; John A. Pople (1998). "Gaussian-3 theory using reduced Møller-Plesset order". The Journal of Chemical Physics (The American Institute of Physics) 110 (10): 4703–4710. doi:10.1063/1.478385. Bibcode: 1999JChPh.110.4703C.
7. ↑ 7.0 7.1 7.2 7.3 Ohlinger, William S.; Philip E. Klunzinger; Bernard J. Deppmeier; Warren J. Hehre (2009). "Efficient Calculation of Heats of Formation". The Journal of Physical Chemistry A (ACS Publications) 113 (10): 2165–2175. doi:10.1021/jp810144q. PMID 19222177. Bibcode: 2009JPCA..113.2165O.
8. ↑ Krylov, Anna I.; Gill, Peter M.W. (2013). "Q-Chem: an engine for innovation". Wiley Interdisciplinary Reviews: Computational Molecular Science 3 (3): 317–326. doi:10.1002/wcms.1122.
9. ↑ Hammond, G. S. (1955). "A Correlation of Reaction Rates". Journal of the American Chemical Society (ACS Publications) 77 (2): 334–338. doi:10.1021/ja01607a027.
10. ↑ Leach, Andrew R. (2001). Molecular modelling: principles and applications. Englewood Cliffs, N.J: Prentice Hall. ISBN 0-582-38210-6.
11. ↑ Thomas A. Halgren (1996). "Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94". Journal of Computational Chemistry 17 (5–6): 490–519. doi:10.1002/(SICI)1096-987X(199604)17:5/6<490::AID-JCC1>3.0.CO;2-P.
12. ↑ Matthew Clark; Richard D. Cramer III; Nicole Van Opdenbosch (1989). "Validation of the general purpose tripos 5.2 force field". Journal of Computational Chemistry 10 (8): 982–1012. doi:10.1002/jcc.540100804.
13. ↑ Michael J. S. Dewar; Walter Thiel (1977). "Ground states of molecules. 38. The MNDO method. Approximations and parameters". Journal of the American Chemical Society (ACS Publications) 99 (15): 4899–4907. doi:10.1021/ja00457a004.
14. ↑ Michael J. S. Dewar; Eve G. Zoebisch; Eamonn F. Healy; James J. P. Stewart (1985). "Development and use of quantum molecular models. 75. Comparative tests of theoretical procedures for studying chemical reactions". Journal of the American Chemical Society (ACS Publications) 107 (13): 3902–3909. doi:10.1021/ja00299a024.
15. ↑ James J. P. Stewart (1989). "Optimization of parameters for semiempirical methods I. Method". The Journal of Computational Chemistry 10 (2): 209–220. doi:10.1002/jcc.540100208.
16. ↑ James J. P. Stewart (1989). "Optimization of parameters for semiempirical methods II. Applications". The Journal of Computational Chemistry 10 (2): 221–264. doi:10.1002/jcc.540100209.
17. ↑ James J. P. Stewart (1991). "Optimization of parameters for semiempirical methods. III Extension of PM3 to Be, Mg, Zn, Ga, Ge, As, Se, Cd, In, Sn, Sb, Te, Hg, Tl, Pb, and Bi". The Journal of Computational Chemistry 12 (3): 320–341. doi:10.1002/jcc.540120306. https://zenodo.org/record/1229233.
18. ↑ James J. P. Stewart (2004). "Optimization of parameters for semiempirical methods IV: extension of MNDO, AM1, and PM3 to more main group elements". The Journal of Molecular Modeling (Springer Berlin-Heidelberg) 10 (2): 155–164. doi:10.1007/s00894-004-0183-z. PMID 14997367.
19. ↑ Gerd B. Rocha; Ricardo O. Freire; Alfredo M. Simas; James J. P. Stewart (2006). "RM1: A reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I". The Journal of Computational Chemistry 27 (10): 1101–1111. doi:10.1002/jcc.20425. PMID 16691568.
20. ↑ James J. P. Stewart (2007). "Optimization of Parameters for Semiempirical Methods V: Modification of NDDO Approximations and Application to 70 Elements". The Journal of Molecular Modeling (Springer) 13 (12): 1173–1213. doi:10.1007/s00894-007-0233-4. PMID 17828561.
21. ↑ 21.0 21.1 Aleksandr V. Marenich; Ryan M. Olson; Casey P. Kelly; Christopher J. Cramer; Donald G. Truhlar (2007). "Self-Consistent Reaction Field Model for Aqueous and Nonaqueous Solutions Based on Accurate Polarized Partial Charges". Journal of Chemical Theory and Computation (ACS Publications) 3 (6): 2011–2033. doi:10.1021/ct7001418. PMID 26636198.
22. ↑ 22.0 22.1 22.2 22.3 A. D. Becke (1988). "Density-functional exchange-energy approximation with correct asymptotic behavior". Physical Review A (American Physical Society) 38 (6): 3098–3100. doi:10.1103/PhysRevA.38.3098. PMID 9900728. Bibcode: 1988PhRvA..38.3098B.
23. ↑ John P. Perdew (1986). "Density-functional approximation for the correlation energy of the inhomogeneous electron gas". Physical Review B (American Physical Society) 33 (12): 8822–8824. doi:10.1103/PhysRevB.33.8822. PMID 9938299. Bibcode: 1986PhRvB..33.8822P.
24. ↑ 24.0 24.1 24.2 Lee, Chengeth; Weitao Yang; Robert G. Parr (1988). "Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density". Physical Review B (American Physical Society) 37 (2): 785–789. doi:10.1103/PhysRevB.37.785. PMID 9944570. Bibcode: 1988PhRvB..37..785L. https://cdr.lib.unc.edu/downloads/p2677460w.
25. ↑ 25.0 25.1 25.2 P. J. Stephens; F. J. Devlin; C. F. Chabalowski; M. J. Frisch (1994). "Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields". The Journal of Physical Chemistry (ACS Publications) 98 (45): 11623–11627. doi:10.1021/j100096a001.
26. ↑ 26.0 26.1 26.2 Ross D. Adamsona, Peter M. W. Gill and John A. Pople (1998). "Empirical density functionals". Chemical Physics Letters (Elsevier) 284 (5–6): 6–11. doi:10.1016/S0009-2614(97)01282-7. Bibcode: 1998CPL...284....6A.
27. ↑ 27.0 27.1 27.2 Peter M. W. Gill, Yeh Lin Ching and Michael W. George (2004). "EDF2: A density functional for predicting molecular vibrational frequencies". Australian Journal of Chemistry (Commonwealth Scientific and Industrial Research Organization) 57 (4): 365–370. doi:10.1071/CH03263.
28. ↑ 28.0 28.1 28.2 Yan Zhao; Donald G. Truhlar (2008). "The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals". Theoretical Chemistry Accounts (Springer Berlin / Heidelberg) 120 (1–3): 215–241. doi:10.1007/s00214-007-0310-x.
29. ↑ 29.0 29.1 J. D. Chai; Martin Head-Gordon (2008). "Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections". Physical Chemistry Chemical Physics (RSC Publishing) 10 (44): 6615–66120. doi:10.1039/b810189b. PMID 18989472. Bibcode: 2008PCCP...10.6615C. https://digital.library.unt.edu/ark:/67531/metadc929924/.
30. ↑ 30.0 30.1 NIST Chemistry WebBook. nist.gov
31. ↑ P.A.M. Dirac (1930). "Note on Exchange Phenomena in the Thomas Atom". Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge Journals) 26 (3): 376–385. doi:10.1017/S0305004100016108. Bibcode: 1930PCPS...26..376D.
32. ↑ Peter M. W. Gill (1996). "A new gradient-corrected exchange functional". Molecular Physics (Taylor & Francis) 89 (2): 433–445. doi:10.1080/00268979609482484. Bibcode: 1996MolPh..89..433G.
33. ↑ A.T.B. Gilbert; P.M.W. Gill (1999). "Decomposition of exchange-correlation energies". Chemical Physics Letters (Elsevier) 312 (5–6): 511–521. doi:10.1016/S0009-2614(99)00836-2. Bibcode: 1999CPL...312..511G.
34. ↑ John P. Perdew; Yue Wang (1992). "Accurate and simple analytic representation of the electron-gas correlation energy". Physical Review B (American Physical Society) 45 (23): 13244–13249. doi:10.1103/PhysRevB.45.13244. PMID 10001404. Bibcode: 1992PhRvB..4513244P.
35. ↑ Vosko, S.H.; Wilk, L.; Nusair, M. (1980). "Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis". Canadian Journal of Physics (NRC Research Press) 58 (8): 1200–1211. doi:10.1139/p80-159. Bibcode: 1980CaJPh..58.1200V. https://cloudfront.escholarship.org/dist/prd/content/qt23j4q7zm/qt23j4q7zm.pdf?t=obcp14.
36. ↑ John P. Perdew; Yue Wang (1992). "Accurate and simple analytic representation of the electron-gas correlation energy". Physical Review B (The American Physical Society) 45 (23): 13244–13249. doi:10.1103/PhysRevB.45.13244. PMID 10001404. Bibcode: 1992PhRvB..4513244P.
37. ↑ J. P. Perdew (1981). "Density-functional approximation for the correlation energy of the inhomogeneous electron gas". Physical Review B (The American Physical Society) 23 (10): 5048–5079. doi:10.1103/PhysRevB.23.5048. Bibcode: 1981PhRvB..23.5048P.
38. ↑ J. P. Perdew; A. Zunger (1986). "Self-interaction correction to density-functional approximations for many-electron systems". Physical Review B (The American Physical Society) 33 (12): 8822–8824. doi:10.1103/PhysRevB.33.8822. PMID 9938299. Bibcode: 1986PhRvB..33.8822P.
39. ↑ John P. Perdew; Kieron Burke; Matthias Ernzerhof (1996). "Generalized Gradient Approximation Made Simple". Physical Review Letters (American Physical Society) 77 (18): 3865–3868. doi:10.1103/PhysRevLett.77.3865. PMID 10062328. Bibcode: 1996PhRvL..77.3865P.
40. ↑ A. D. Becke; M. R. Roussel (1989). "Exchange holes in inhomogeneous systems: A coordinate-space model". Physical Review A (The American Physical Society) 39 (8): 3761–3767. doi:10.1103/PhysRevA.39.3761. PMID 9901696. Bibcode: 1989PhRvA..39.3761B.
41. ↑ A. Daniel Boese; Jan M. L. Martin (2004). "Development of density functionals for thermochemical kinetics". The Journal of Chemical Physics 121 (8): 3405–3417. doi:10.1063/1.1774975. PMID 15303903. Bibcode: 2004JChPh.121.3405B.
42. ↑ Truhlar Group
43. ↑ 43.0 43.1 Yan Zhao; Nathan E. Schultz; Donald G. Truhlar (2006). "Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parameterization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions". Journal of Chemical Theory and Computation (ACS Publications) 2 (2): 364–382. doi:10.1021/ct0502763. PMID 26626525.
44. ↑ Yan Zhao; Donald G. Truhlar (2008). "A new local density functional for main-group thermochemistry, transition metal bonding, thermochemical kinetics, and noncovalent interactions". The Journal of Chemical Physics (American Institute of Physics) 125 (19): 194101–194119. doi:10.1063/1.2370993. PMID 17129083. Bibcode: 2006JChPh.125s4101Z.
45. ↑ Yan Zhao; Donald G. Truhlar (2008). "Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States". The Journal of Physical Chemistry A (ACS Publications) 110 (49): 13126–13130. doi:10.1021/jp066479k. PMID 17149824. Bibcode: 2006JPCA..11013126Z.
46. ↑ Head-Gordon Group
47. ↑ 47.0 47.1 Jeng-Da Chai; Martin Head-Gordon (2006). "Systematic optimization of long-range corrected hybrid density functionals". The Journal of Chemical Physics (American Institute of Physics) 128 (8): 084106–084121. doi:10.1063/1.2834918. PMID 18315032. Bibcode: 2008JChPh.128h4106C. http://ntur.lib.ntu.edu.tw/bitstream/246246/221148/-1/05.pdf.
48. ↑ George D. Purvis; Rodney J. Bartlett (1982). "A full coupled-cluster singles and doubles model: The inclusion of disconnected triples". The Journal of Chemical Physics (The American Institute of Physics) 76 (4): 1910–1919. doi:10.1063/1.443164. Bibcode: 1982JChPh..76.1910P.
49. ↑ Krishnan Raghavachari; Gary W. Trucks; John A. Pople and; Martin Head-Gordon (1989). "A fifth-order perturbation comparison of electron correlation theories". Chemical Physics Letters (Elsevier Science) 157 (6): 479–483. doi:10.1016/S0009-2614(89)87395-6. Bibcode: 1989CPL...157..479R.
50. ↑ Troy Van Voorhis; Martin Head-Gordon (2001). "Two-body coupled cluster expansions". The Journal of Chemical Physics (The American Institute of Physics) 115 (11): 5033–5041. doi:10.1063/1.1390516. Bibcode: 2001JChPh.115.5033V.
51. ↑ C. David Sherrill; Anna I. Krylov; Edward F. C. Byrd; Martin Head-Gordon (1998). "Energies and analytic gradients for a coupled-cluster doubles model using variational Brueckner orbitals: Application to symmetry breaking in O+4". The Journal of Chemical Physics (The American Institute of Physics) 109 (11): 4171–4182. doi:10.1063/1.477023. Bibcode: 1998JChPh.109.4171S.O+4&rft.jtitle=The+Journal+of+Chemical+Physics&rft.aulast=C.+David+Sherrill&rft.au=C.+David+Sherrill&rft.au=Anna+I.+Krylov&rft.au=Edward+F.+C.+Byrd&rft.au=Martin+Head-Gordon&rft.date=1998&rft.volume=109&rft.issue=11&rft.pages=4171–4182&rft.pub=The+American+Institute+of+Physics&rft_id=info:doi/10.1063/1.477023&rft_id=info:bibcode/1998JChPh.109.4171S&rfr_id=info:sid/en.wikibooks.org:Software:Spartan_(chemistry_software)">
52. ↑ Steven R. Gwaltney; Martin Head-Gordon (2000). "A second-order correction to singles and doubles coupled-cluster methods based on a perturbative expansion of a similarity-transformed Hamiltonian". Chemical Physics Letters (Elsevier) 323 (1–2): 21–28. doi:10.1016/S0009-2614(00)00423-1. Bibcode: 2000CPL...323...21G.
53. ↑ Troy Van Voorhis; Martin Head-Gordon (2000). "The quadratic coupled cluster doubles model". Chemical Physics Letters (Elsevier) 330 (5–6): 585–594. doi:10.1016/S0009-2614(00)01137-4. Bibcode: 2000CPL...330..585V.
54. ↑ 54.0 54.1 54.2 Anna I. Krylov; C. David Sherrill; Edward F. C. Byrd; Martin Head-Gordon (1998). "Size-consistent wave functions for nondynamical correlation energy: The valence active space optimized orbital coupled-cluster doubles model". The Journal of Chemical Physics (The American Institute of Physics) 109 (24): 10669–10678. doi:10.1063/1.477764. Bibcode: 1998JChPh.10910669K.
55. ↑ 55.0 55.1 Chr. Møller; M. S. Plesset (1934). "Note on an Approximation Treatment form Many-Electron Systems". Physical Review (The American Physical Society) 46 (7): 618–622. doi:10.1103/PhysRev.46.618. Bibcode: 1934PhRv...46..618M. https://authors.library.caltech.edu/1753/1/MOLpr34.pdf.
56. ↑ Head-Gordon, Martin; Pople, John A.; Frisch, Michael J. (1988). "MP2 energy evaluation by direct methods". Chemical Physics Letters 153 (6): 503–506. doi:10.1016/0009-2614(88)85250-3. Bibcode: 1988CPL...153..503H.
57. ↑ Pople, J. A.; Seeger, R.; Krishnan, R. (1977). "Variational configuration interaction methods and comparison with perturbation theory". International Journal of Quantum Chemistry 12 (S11): 149–163. doi:10.1002/qua.560120820.
58. ↑ Pople, John A.; Binkley, J. Stephen; Seeger, Rolf (1976). "Theoretical models incorporating electron correlation". International Journal of Quantum Chemistry 10 (S10): 1–19. doi:10.1002/qua.560100802.
59. ↑ Krishnan Raghavachari; John A. Pople (1978). "Approximate fourth-order perturbation theory of the electron correlation energy". International Journal of Quantum Chemistry 14 (1): 91–100. doi:10.1002/qua.560140109.
60. ↑ Martin Feyereisena, George Fitzgeralda; Andrew Komornickib (1993). "Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods". Chemical Physics Letters (Elsevier) 208 (5–6): 359–363. doi:10.1016/0009-2614(93)87156-W. Bibcode: 1993CPL...208..359F.
61. ↑ Florian Weigend; Marco Häser (1997). "RI-MP2: first derivatives and global consistency". Theoretical Chemistry Accounts (Springer Berlin / Heidelberg) 97 (1–4): 331–340. doi:10.1007/s002140050269.
62. ↑ Robert A. Distasio J.R.; Ryan P. Steele; Young Min Rhee; Yihan Shao; Martin Head-Gordon (2007). "An improved algorithm for analytical gradient evaluation in resolution-of-the-identity second-order Møller-Plesset perturbation theory: Application to alanine tetrapeptide conformational analysis". Journal of Computational Chemistry 28 (5): 839–856. doi:10.1002/jcc.20604. PMID 17219361.
63. ↑ 63.0 63.1 Erich Runge; E. K. U. Gross (1984). "Density-Functional Theory for Time-Dependent Systems". Physical Review Letters (American Physical Society) 52 (12): 997–1000. doi:10.1103/PhysRevLett.52.997. Bibcode: 1984PhRvL..52..997R.
64. ↑ 64.0 64.1 So Hirata; Martin Head-Gordon (1999). "Time-dependent density functional theory for radicals: An improved description of excited states with substantial double excitation character". Chemical Physics Letters (Elsevier) 302 (5–6): 375–382. doi:10.1016/S0009-2614(99)00137-2. Bibcode: 1999CPL...302..375H.
65. ↑ 65.0 65.1 David Maurice; Martin Head-Gordon (1999). "Analytical second derivatives for excited electronic states using the single excitation configuration interaction method: theory and application to benzo[a]pyrene and chalcone". Molecular Physics (Taylor & Francis) 96 (10): 1533–1541. doi:10.1080/00268979909483096. Bibcode: 1999MolPh..96.1533M.
66. ↑ 66.0 66.1 Martin Head-Gordon; Rudolph J. Rico; Manabu Oumi; Timothy J. Lee (1994). "A doubles correction to electronic excited states from configuration interaction in the space of single substitutions". Chemical Physics Letters (Elsevier) 219 (1–2): 21–29. doi:10.1016/0009-2614(94)00070-0. Bibcode: 1994CPL...219...21H. https://zenodo.org/record/1253844.
67. ↑ 67.0 67.1 John A. Pople; Martin Head-Gordon; Krishnan Raghavachari (1987). "Quadratic configuration interaction. A general technique for determining electron correlation energies". The Journal of Chemical Physics (American Institute of Physics) 87 (10): 5968–35975. doi:10.1063/1.453520. Bibcode: 1987JChPh..87.5968P.
68. ↑ 68.0 68.1 Rhee, Young Min; Martin Head-Gordon (2007). "Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods". The Journal of Physical Chemistry A (ACS Publications) 111 (24): 5314–5326. doi:10.1021/jp068409j. PMID 17521172. Bibcode: 2007JPCA..111.5314R. https://digital.library.unt.edu/ark:/67531/metadc925761/.
69. ↑ Larry A. Curtiss; Krishnan Raghavachari; Gary W. Trucks; John A. Pople (1991). "Gaussian-2 theory for molecular energies of first- and second-row compounds". The Journal of Chemical Physics (The American Institute of Physics) 94 (11): 7221–7231. doi:10.1063/1.460205. Bibcode: 1991JChPh..94.7221C.
70. ↑ Larry A. Curtiss; Krishnan Raghavachari; Paul C. Redfern; Vitaly Rassolov; John A. Pople (1998). "Gaussian-3 (G3) theory for molecules containing first and second-row atoms". The Journal of Chemical Physics (The American Institute of Physics) 109 (18): 7764–7776. doi:10.1063/1.477422. Bibcode: 1998JChPh.109.7764C.
71. ↑ 71.0 71.1 71.2 71.3 71.4 71.5 71.6 Spartan Tutorial & User's Guide Hehre, Warren J.; Ohlinger, William S. (2013). Spartan'14 Tutorial and User's Guide. Irvine, California: Wavefunction, Inc..
72. ↑ 72.0 72.1 72.2 72.3 [1] An assessment of most computational models is available. Hehre, Warren J. (2003). A Guide to Molecular Mechanics and Quantum Chemical Calculations. Irvine, California: Wavefunction, Inc.. ISBN 1-890661-06-6.
73. ↑ Alan J. Shusterman; Gwendolyn P. Shusterman (1997). "Teaching Chemistry with Electron Density Models". The Journal of Chemical Education (ACS Publications) 74 (7): 771–775. doi:10.1021/ed074p771. Bibcode: 1997JChEd..74..771S.
74. ↑ Hehre, Warren J.; Alan Shusterman; Janet Nelson (1998). Molecular Modeling Workbook for Organic Chemistry. Wavefunction, Inc.. ISBN 1-890661-06-6.
75. ↑ Smith, Michael B. (2010). Organic Synthesis, 3rd Edition. Wavefunction, Inc.. pp. CH.2 & CH.11 modeling problems. ISBN 978-1-890661-40-3.
76. ↑ Kimberly J. Linenberger; Renee S. Cole; Somnath Sarkar (2011). "Looking Beyond Lewis Structures: A General Chemistry Modeling Experiment Focusing on Physical Properties and Geometry". The Journal of Chemical Education (ACS Publications) 88 (7): 962–965. doi:10.1021/ed100727r. Bibcode: 2011JChEd..88..962L.
77. ↑ Hyosub Kim; Segun Sulaimon; Sandra Menezes; Anne Son; Warren J. C. Menezes (2011). "A Comparative Study of Successful Central Nervous System Drugs Using Molecular Modeling". The Journal of Chemical Education (ACS Publications) 88 (10): 1389–1393. doi:10.1021/ed100824u. Bibcode: 2011JChEd..88.1389K.
78. ↑ Anthony P. Scott; Leo Radom (1996). "Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors". The Journal of Physical Chemistry (ACS Publications) 100 (41): 16502–16513. doi:10.1021/jp960976r.
79. ↑ Benny G. Johnson; Jan Florián (1995). "The prediction of Raman spectra by density functional theory. Preliminary findings". Chemical Physics Letters (Elsevier) 47 (1–2): 120–125. doi:10.1016/0009-2614(95)01186-9. Bibcode: 1995CPL...247..120J.
80. ↑ 80.0 80.1 Jorg Kussman; Christian Ochsenfeld (2007). "Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory". The Journal of Chemical Physics (American Institute of Physics) 127 (5): 054103. doi:10.1063/1.2749509. PMID 17688330. Bibcode: 2007JChPh.127e4103K.
81. ↑ 81.0 81.1 Krzysztof Wolinski; James F. Hinton; Peter Pulay (1990). "Efficient implementation of the gauge-independent atomic orbital method for NMR chemical shift calculations". Journal of the American Chemical Society (ACS Publications) 112 (23): 8251–8260. doi:10.1021/ja00179a005.
82. ↑ Silverstein, Robert M.; Francis X. Webster; David J. Kiemle (2005). Spectroscopy Identification of Organic Compounds. John Wiley & Sons, Inc.. pp. 250–254, 259, 267. ISBN 978-0-471-39362-7.
83. ↑ Keeler, James (2010). Understanding NMR Spectroscopy. John Wiley & Sons, Inc.. pp. 209–215. ISBN 978-0-470-74608-0.
84. ↑ Silverstein, Robert M.; Francis X. Webster; David J. Kiemle (2005). Spectroscopy Identification of Organic Compounds. John Wiley & Sons, Inc.. pp. 254–263. ISBN 978-0-471-39362-7.
85. ↑ John A. Pople; Martin Head-Gordon; Krishnan Raghavachari (1987). "Quadratic configuration interaction. A general technique for determining electron correlation energies". The Journal of Chemical Physics (American Institute of Physics) 87 (10): 5968–35975. doi:10.1063/1.453520. Bibcode: 1987JChPh..87.5968P.
86. ↑ McDonald, R. S.; Paul A. Wilks (1988). "JCAMP-DX: A Standard Form for Exchange of Infrared Spectra in Computer Readable Form". Applied Spectroscopy (Society for Applied Spectroscopy) 42 (1): 151–162. doi:10.1366/0003702884428734. Bibcode: 1988ApSpe..42..151M.
87. ↑ 87.0 87.1 Ditchfield, R; Hehre, W.J; Pople, J. A. (1971). "Self-Consistent Molecular-Orbital Methods. IX. An Extended Gaussian-Type Basis for Molecular-Orbital Studies of Organic Molecules". J. Chem. Phys. 54 (2): 724–728. doi:10.1063/1.1674902. Bibcode: 1971JChPh..54..724D.
88. ↑ [2] NMRShiftDB.
89. ↑ Allen, Frank (2002). "The Cambridge Structural Database: a quarter of a million crystal structures and rising". Acta Crystallogr. B 58 (3): 380–388. doi:10.1107/S0108768102003890. PMID 12037359.

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